$\frac {|a-b|+|b-a|}{|a|+|b|} = ?$

Question

$$a<0<b$$

$$\frac {|a-b|+|b-a|}{|a|+|b|} = ?$$

Let me show my thinkings

If $a<0<b$ then $a$ must be negative. If we look at $b$, it must be positive too. However, I still doubt it.

Kindest Regards

Answer 1

since we have $$a<0<b$$ and we have $$b-a>0$$ and the term is given by $$\frac{2|b-a|}{b-a}=\frac{2(b-a)}{b-a}=2$$